On Inflation and the Persistence of shocks to Output

The purpose of this paper is to examine whether the level of inflation matters for the persistence of output growth when shocks to output have asymmetric effects. The idea that inflation could have such threshold effects is worth investigating because some authors have suggested that a low inflation environment was instrumental in generating the unprecedented strong and sustained output growth rates recently witnessed in some countries. In a separate literature the debate has been ongoing with respect to whether shocks to output growth have asymmetric effects on its persistence. For example, Beaudry and Koop (1993) have shown that, by including an index variable that captures the depth of recessions in a standard ARMA model, positive shocks yield a substantially different effect on output dynamics than negative ones. On the other hand, using unobserved-component models with a threshold variable, Elwood (1998) finds that these two types of shocks do not lead to significantly different estimates of output growth persistence. This discrepancy in results may lie in the fact that these models are not general enough. Thus, a good strategy would be to combine elements from both studies and to use a more flexible modeling framework to examine this asymmetry question. In this paper we generalize the Elwood (1998) model by extending it to an ARMA setting while allowing for multiple threshold effects. Using Canadian data we then test for inflation threshold effects on output growth dynamics, as well as for asymmetric impacts of output shocks. The dynamics parameters are therefore assumed to change depending on 1) whether lagged disturbances are positive or negative, and 2) on whether inflation is above or below some estimated threshold level. The estimation is carried out using maximum likelihood and Kalman filtering while hypotheses are tested via the application of tests developed by Hansen (1996) for when a nuisance parameter is present only under the alternative. Our first result concurs with that of Beaudry and Koop and shows that positive shocks indeed lead to a significantly higher output growth persistence than do negative shocks. In addition we find that, with positive shocks, the asymmetry is more marked when inflation is above its threshold value; that is, while negative shocks display a similar persistence, positive shocks to output are more persistent when inflation is in the low regime than when it is in the high one. Therefore, low inflation can be associated with a healthier output growth dynamics compared to an environment of high inflation. Finally, we find the interesting result that the estimated threshold value for Canada is approximately 4%, which is one per cent higher than the upper limit of the Bank of Canada announced inflation target bands for the post-1996 period.